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单词 IdealTriangle
释义

ideal triangle


In hyperbolic geometry, an ideal triangle is a set of three lines which connect three distinct points on the boundary of the model of hyperbolic geometry.

Below is an example of an ideal triangle in the Beltrami-Klein model:

Below is an example of an ideal triangle in the Poincaré disc model:

Below are some examples of ideal triangles in the upper half plane model:

speaking, none of these figures are triangles in hyperbolic geometry; however, ideal triangles are useful for proving that, given r with 0<r<π, there is a triangle in hyperbolic geometry whose angle sum in radians is equal to r.

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更新时间:2025/5/4 2:53:24